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Generalized linear and nonlinear mixed-effects models are used extensively in biomedical, social, and agricultural sciences. The statistical analysis of these models is based on the asymptotic properties of the maximum likelihood estimator. However, it is usually assumed that the maximum likelihood estimator is consistent, without providing a proof. A rigorous proof of the consistency by verifying...
We consider a class of random effects models for clustered multivariate binary data based on the threshold crossing technique of a latent random vector. Components of this latent vector are assumed to have a Laird–Ware structure. However, in place of their Gaussian assumptions, any specified class of multivariate distribution is allowed for the random effects, and the error vector is allowed to have...
Lately mixed models are heavily employed in analyses of promotional tactics as well as in clinical research. The Best Linear Unbiased Predictor (BLUP) in mixed models is a function of the variance components, which are typically estimated using conventional MLE based methods. It is well known that such approaches frequently yield estimates of factor variances that are either zero or negative. In such...
This paper considers predictions of vectors of parameters under a general linear model $$\mathbf{y}= \mathbf{X}{\pmb {\beta }}+ {\pmb {\varepsilon }}$$ y = X β + ε with the random coefficients $${\pmb {\beta }}$$ β satisfying $${\pmb {\beta }}=\mathbf{A}{\pmb {\alpha }}+ {\pmb {\gamma }}$$ β = A α + γ . It utilizes a standard method of solving constrained...
In the paper, a simple projection-based method is systematically developed to estimate the qth ( $$q\ge 2$$ q ≥ 2 ) order moments of random effects and errors in the ANOVA type mixed model (ANOVAMM), where the response may not be divided into independent sub-vectors. All the estimates are weakly consistent and the second-order moment estimates are strongly consistent. Besides, the derived...
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